Distance to overtake

[scubbasteevo]

Good evening. This is a college algebra story problem:
"A private airplane leaves Midway Airport and flies due east @ 180 km/h. Two hours later, another jet leaves midway and flies due east @ 900 km/h. How far from the airport will the jet overtake the private plane? "

-I know "overtake" doesn't mean pass, but rather "how long it will take for the planes to meet up".
-I have set up a table of the information as such:

a = private jet @ 180 km/h
b = jetliner @ 900 km/ h - 2 hours later
- I know the distance formula is D=rt, and I have read several 'help' topics which have only confused me more. I'm not sure how to set it up if it goes in the form of a=b+2 or something like that? Or if it's substituting one variable for another and solving for said variable. Your help is greatly appreciated and hopefully comes quick. But I understand you have lives. Thank you!
Steve

 

[stapel]

"A private airplane leaves Midway Airport and flies due east @ 180 km/h. Two hours later, another jet leaves midway and flies due east @ 900 km/h. How far from the airport will the jet overtake the private plane? "

-I have set up a table of the information as such:

a = private jet @ 180 km/h
b = jetliner @ 900 km/ h - 2 hours later

- I know the distance formula is D=rt....

Whatever "table" you set up didn't translate onto the page; all we're seeing is a listing of information...?

A table is actually quite helpful, so try using: a table, the "distance" equation, and the given information. :wink:

+---------+------+-------+-------+
|#########|  D   =   r   *   t   |
+---------+------+-------+-------+
| private |      |  180  |   t   |
+---------+------+-------+-------+
|   jet   |      |  900  | t - 2 |
+---------+------+-------+-------+

Then note that D = rt, and multiply the values and expressions for "r" and "t". Then note that, since the planes covered the same distance (from take-off to over-take point), the two distances are equal. Set the distances equal, and solve for the time t. Back-solve for the distance. :idea:

Have fun!

Eliz.

 

[soroban]

Hello, Steve!

Here's another approach . . .

A private airplane leaves Midway Airport and flies due east at 180 km/hr.
Two hours later, another jet leaves Midway and flies due east at 900 km/hr.
How far from the airport will the jet overtake the private plane?

The private plane has a two-hour headstart; it has already traveled 360 miles.

Relative to the private plane, the jet is flying at: .900 - 180 .= .720 km/hr.
. . It is as if the private plane has stopped and the jet is approaching it at 720 km/hr.

To travel the 360 miles, it will take the jet plane: .360/720 = 1/2 hour.

In that time, the jet plane has traveled: .(1/2)(900) .= .450 km